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In this paper, we investigate two types of time-harmonic elastic wave scattering problems. The first one involves the scattered wave generated by an active elastic source with compact support. The second one concerns elastic wave scattering…

Analysis of PDEs · Mathematics 2025-08-11 Huaian Diao , Xiaoxu Fei , Hongyu Liu

In this paper, we present the first well-posedness result for elastic scattering by locally rough interfaces in both two and three dimensions. Inspired by the Helmholtz decomposition, we discover a fundamental identity for the stress…

Analysis of PDEs · Mathematics 2026-01-21 Chengyu Wu , Yushan Xue , Jiaqing Yang

We derive an analytical expression for the scattering of a scalar wave from a perfectly conducting self-affine one dimensional surface in the framework of the Kirchhoff approximation. We show that most of the results can be recovered via a…

Other Condensed Matter · Physics 2009-11-10 Ingve Simonsen , Damien Vandembroucq , Stephane Roux

This paper concerns the random source problems for the time-harmonic acoustic and elastic wave equations in two and three dimensions. The goal is to determine the compactly supported external force from the radiated wave field measured in a…

Analysis of PDEs · Mathematics 2018-12-03 Jianliang Li , Tapio Helin , Peijun Li

We present different classes of initial data to the three-dimensional, incompressible Navier-Stokes equations, which generate a global in time, unique solution though they may be arbitrarily large in the end-point function space in which a…

Analysis of PDEs · Mathematics 2012-06-01 Jean-Yves Chemin , Isabelle Gallagher , Chloé Mullaert

This paper is concerned with the analysis of elastic wave scattering of a time-harmonic plane wave by a biperiodic rigid surface, where the wave propagation is governed by the three-dimensional Navier equation. An exact transparent boundary…

Numerical Analysis · Mathematics 2016-11-18 Xue Jiang , Peijun Li , Junliang Lv , Weiying Zheng

In this paper, we consider the scattering of a plane wave by a rigid obstacle embedded in a homogeneous and isotropic elastic medium in three dimensions. Based on the Helmholtz decomposition, the elastic scattering problem is reduced to a…

Numerical Analysis · Mathematics 2022-09-14 Heping Dong , Jun Lai , Peijun Li

The simplest Lorentz-nonreciprocal medium has the constitutive relations (${\bf D} =\epso {\bf E} -{\bf \Gamma}\times {\bf H}$ and ${\bf B} =\muo {\bf H} + {\bf \Gamma}\times{\bf E}$). Scattering by a three-dimensional object composed of…

Consider the elastic scattering of a time-harmonic wave by multiple well separated rigid particles in two dimensions. To avoid using the complex Green's tensor of the elastic wave equation, we utilize the Helmholtz decomposition to convert…

Numerical Analysis · Mathematics 2020-08-17 Jun Lai , Peijun Li

The small perturbations method has been extensively used for waves scattering by rough surfaces. The standard method developped by Rice is difficult to apply when we consider second and third order of scattered fields as a function of the…

Condensed Matter · Physics 2009-10-31 A. Soubret , G. Berginc , C. Bourrely

A method is given for evaluating electromagnetic scattering by an irregular surface with spatially-varying impedance. This uses an operator expansion with respect to impedance variation and allows examination of its effects and the…

Classical Physics · Physics 2021-02-02 N. S. Basra , M. Spivack , O. Rath Spivack

The first part of this paper is concerned with the uniqueness to inverse time-harmonic elastic scattering from bounded rigid obstacles in two dimensions. It is proved that a connected polygonal obstacle can be uniquely identified by the…

Analysis of PDEs · Mathematics 2019-09-04 Johannes Elschner , Guanghui Hu

This paper is concerned with an inverse scattering problem for the time-harmonic elastic wave equation with a random potential. Interpreted as a distribution, the potential is assumed to be a microlocally isotropic generalized Gaussian…

Analysis of PDEs · Mathematics 2021-03-23 Jianliang Li , Peijun Li , Xu Wang

We consider a model problem of the scattering of linear acoustic waves in free homogeneous space by an elastic solid. The stress tensor in the solid combines the effect of a linear dependence of strains with the influence of an existing…

Numerical Analysis · Mathematics 2018-04-23 Thomas S. Brown , Tonatiuh Sánchez-Vizuet , Francisco-Javier Sayas

Generalized impedance boundary conditions are effective, approximate boundary conditions that describe scattering of waves in situations where the wave interaction with the material involves multiple scales. In particular, this includes…

Numerical Analysis · Mathematics 2020-05-29 Lehel Banjai , Christian Lubich , Joerg Nick

The elastic properties of a material are encoded in a stiffness tensor field and the propagation of elastic waves is modeled by the elastic wave equation. We characterize analytic and algebraic properties a general anisotropic stiffness…

Differential Geometry · Mathematics 2025-11-21 Joonas Ilmavirta , Pieti Kirkkopelto , Antti Kykkänen

We study the Cauchy problem for the radial energy critical nonlinear wave equation in three dimensions. Our main result proves almost sure scattering for radial initial data below the energy space. In order to preserve the spherical…

Analysis of PDEs · Mathematics 2020-06-17 Bjoern Bringmann

By the use of Green's second integral identity we determine the field scattered from a two-dimensional randomly rough isotropic or anisotropic Dirichlet or Neumann surface when it is illuminated by a scalar Gaussian beam. The integral…

We consider a linearized inverse scattering problem for elastic waves. We prove that a fully anisotropic perturbation of the elastic parameters around an isotropic and homogeneous reference can be uniquely determined by (single-)scattered…

Analysis of PDEs · Mathematics 2026-05-01 Matti Lassas , Shiqi Ma , Lauri Oksanen , Mikko Salo , Jian Zhai

Consider the scattering of a time-harmonic elastic plane wave by a bi-periodic rigid surface. The displacement of elastic wave motion is modeled by the three-dimensional Navier equation in an open domain above the surface. Based on the…

Numerical Analysis · Mathematics 2020-07-28 Gang Bao , Xue Jiang , Peijun Li , Xiaokai Yuan